The database currently contains all extension fields of $\Q_p$ of degree $n$ up to isomorphism for primes $p<150$ and $1\leq n \leq 11$.

Browse local number fields

The table gives for each $p$ and $n$ shown, the number of degree $n$ extension fields of $\Q_p$ up to isomorphism.

$p$ \ $n$ 2 3 4 5 6 7 8 9 10 11
2 7 2 59 2 47 2 1823 3 158 2
3 3 10 5 2 75 2 8 795 6 2
5 3 2 7 26 7 2 11 3 258 2
7 3 4 5 2 12 50 8 7 6 2
11 3 2 5 6 7 2 8 3 18 122
13 3 4 7 2 12 2 11 7 6 2
17 3 2 7 2 7 2 15 3 6 2
19 3 4 5 2 12 2 8 13 8 2
23 3 2 5 2 7 2 8 3 6 12

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Degree: e.g. 6, or a range like 3..5
Prime $p$ for base field $\Q_p$: e.g. 3, or a range like 3..7
Discriminant exponent $c$ : e.g. 8, or a range like 2..6
Ramification index $e$ : e.g. 3, or a range like 2..6
Galois group $G$ : e.g. 5T3, C4, or a list of labels
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